1. Field of the Invention
This invention relates to modeling fissile systems for providing nuclear criticality analyses.
2. Description of Related Art
Nuclear criticality analyses such as criticality analyses of shipping containers, process equipment, and facility process equipment interactions, for example, are used to ensure acceptable safety levels in, for example, nuclear fuel processing facilities. In particular, geometric modeling may be provided in connection with Monte Carlo methods for evaluating the various interactions within a fissile system. Geometric modeling for use with Monte Carlo methods has become a primary analytical tool in nuclear criticality safety analyses, with the use of such geometric modeling extended more frequently to complex structures and arrays. Further, increased regulatory requirements, especially in analyses of shipping containers and equipment, process or facility interactions has increased the need for using such geometric modeling in connection with Monte Carlo methods for providing criticality analyses. Further, this analyses often requires complex modeling of areas of fissile systems with little or no geometric symmetry.
With respect to a criticality analyses of fissile systems, geometric modeling may be used to estimate the effective neutron multiplication factor (k-effective, or keff), which represents the degree to which the neutron population is either increasing or decreasing, thus indicating whether the defined fissile system being modeled approaches or exceeds a sustained nuclear chain reaction. A system that exceeds a sustained nuclear chain reaction is said to be “supercritical” and is identified by a k-effective >1.0. A system that just reaches a sustained nuclear chain reaction is said to be “critical” and is identified by a k-effective that is exactly equal to 1.00. Likewise, in nuclear criticality safety analyses, it is typical to demonstrate the system k-effective is <1.0 (e.g., “subcritical”) with an adequate safety margin such that even under accident conditions the system remains subcritical. By using Monte Carlo methods to track neutrons through a model of a fissile system to estimate k-effective, a determination may be made as to whether the modeled fissile system is, for example, critical, supercritical or subcritical.
Analytic approaches to modeling fissile systems using Monte Carlo methods are limited in their ability to model the precise geometries involved. In particular, these analytic methods are limited in their ability to model complex geometries (e.g., triangular lattices of rods and spheres), as well as in their ability to combine the various geometries (e.g., combine overlapping lattices). It is important to model certain complex geometrical units such as triangular lattices of rods or spheres because these complex geometrical units often represent the most reactive worst-case conditions in criticality safety analyses. Further, the size of rods and spheres may become very small under optimum conditions, requiring the modeling of large numbers of rods or spheres. Thus, the complexity and difficulty of the modeling increases rapidly when small-dimensioned geometric shapes are required to entirely fill a much larger region.
Further, when modeling systems having complex geometric shapes, simple geometric shapes are used to create these complex geometries, which can reduce the accuracy of the modeling. Also, because of the limited capabilities of current analytic approaches to modeling, for example, embedded geometries such as lattices inside (e.g., contained within) other geometrical units require large amounts of run-time memory. Further, to efficiently perform calculations wherein very large numbers (e.g., millions) of individual geometrical units are required to fill a region, large amounts of run-time memory also can be required. As a result, extra processor power is needed to perform the complex calculations, for example, to search each geometrical unit in a lattice to determine where interactions or boundary crossings occur. Further, with respect to criticality analyses of heterogeneous lattices in, for example, shipping containers and facility interactions using known modeling systems, the cost for such analyses often exceeds reasonable limits as a result of the amount of computer time and/or the amount of processing power required to perform the calculations.